Wave solutions and vibration control for the coupled vibration of a moving string system subjected to periodic excitations. (15th April 2023) - He, Yuteng; Chen, Enwei; Ferguson, Neil S.; Zhu, Weidong; Wu, Yuanfeng; Lu, Yimin
Highlights: Obtain wave solutions of a moving string for forced vibration. Explain the coupled vibration between different regions of the moving string. Reveal the transmission and reflection of propagating waves at constraints. Propose a control strategy for vibration suppression of a specified region. Abstract: This paper provides wave solutions for the forced vibration response of a moving string system. Coupled vibration for different regions of the moving string system are considered. Firstly, due to the regularity of transmission and reflection, wave solutions are obtained by D'Alembert's method incorporating forced waves. Secondly, the case of an applied control force provides a control strategy that changes the transmission of propagating waves to prevent the impact of the vibration travelling from one region of the string into another. Thirdly, the coupled vibration issue is handled from the point of view of propagating waves. The transmission and reflection of propagating waves at constraints are also studied. Finally, the theory proposed is applied to two real-life examples, i.e., the wiresaw manufacturing process and the hot-dip galvanizing process. Vibration characteristics of the system with a concentrated or uniform harmonic excitation are studied, and a good performance of the control strategy is demonstrated.